The 29-year-old was a favourite of Jose Mourinho when the Portuguese was in charge at Stamford Bridge, and it is understood that he tried to sign him for United in the summer of 2016.
Willian has appeared in all 17 of Chelsea's Premier League matches this season, but he has started just eight of those fixtures as Blues boss Antonio Conte continues to rotate the attacker.
According to the Daily Mail, United have made an enquiry for Willian ahead of the January transfer window, but Chelsea are reluctant to sell to a direct rival at the mid-point of a season.
The same report, however, claims that an 'extraordinary offer' could force Chelsea to part with the Brazil international when the winter transfer window opens for business.
Willian has scored six goals and registered four assists in all competitions for his London club this season.